A Simulation Tool for Radiative Heat Exchangers

Transcription

1 Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2012 A Simulation Tool for Radiative Heat Exchangers Yunho Hwang yhhwang@umd.edu Jiazhen Ling Reinhard Radermacher Follow this and additional works at: Hwang, Yunho; Ling, Jiazhen; and Radermacher, Reinhard, "A Simulation Tool for Radiative Heat Exchangers" (2012). International Refrigeration and Air Conditioning Conference. Paper This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at Herrick/Events/orderlit.html

2 2324, Page 1 A Simulation Tool for Radiative Heat Exchangers Jiazhen LING, Yunho HWANG*, Vikrant AUTE, Reinhard RADERMACHER Center for Environmental Energy Engineering Department of Mechanical Engineering, University of Maryland 4164 Glenn L. Martin Hall Bldg., College Park, MD 20742, USA * Corresponding Author, Tel: (301) , yhhwang@umd.edu ABSTRACT In order to minimize the large fan power demand from low temperature lift heat pump systems, a radiative heat exchanger is proposed as an indoor heat exchanger design in such systems. The radiative heat exchanger utilizes both natural convection and radiation so that it is capable of reducing fan power consumption while simultaneously providing an improved thermal comfort. A software tool has been developed to simulate the operative temperature field created by a radiative heat exchanger installed in a typical office setting (3m by 3m by 3m dimension). The tool includes the modeling of mean radiant temperature using an eight-surface (six walls, a window and a sunlit area on the floor) assumption, as well as the modeling of air temperature using proper orthogonal decomposition method. The proper orthogonal decomposition method was shown to be more computationally cost-effective than the conventional CFD simulation. Finally, the operative temperature simulation results were validated with the experimental data, showing the average discrepancy of 0.4 K in four measurement locations. 1. INTRODUCTION In a vapor compression system, as the temperature difference between heat absorption and heat rejection processes decreases, the coefficient of performance (COP) of the system generally increases. It is caused by the fact that the reduced temperature difference helps decreasing the pressure lift of the compressor and furthermore decreasing the power input to the compressor. To reduce the temperature lift, one can increase the evaporating temperature or decrease the condensing temperature or both. However, the increase in the evaporating temperature has to reach a limitation above which no dehumidification occurs in the system. Further research manages to remove the limitation by applying the separate sensible and latent cooling technology (SSLC) (Ling et al., 2010). Despite the encouraging energy savings reported in the literature, the design of the indoor heat exchanger (HX) in the SSLC system remains a challenge. As the refrigerant evaporating temperature increases, the supply air temperature usually increases for a given HX. Consequently, the air mass flow rate has to increase to maintain the system capacity. The increased air flow rate leads to an increased fan power consumption and may offset the power savings by the compressor. In short, how to design an indoor HX that minimizes the fan power demand is the challenge. There are various HX designs which address such a challenge, and among those, chilled ceiling panels and heated floor systems are under most discussions. For both products, the heat transfer mechanism between the working fluid and indoor air is natural convection and radiation, and therefore, the fan power demand is almost zero. Moreover, the enlarged heat transfer area of those products provides radiant cooling or heating to the occupants so that both products may provide better thermal comfort than conventional indoor HXs. However, the installation of the two systems requires an overhaul of the existing ceiling and floor and hence cannot be done without a significant impact to residents (see Figure 1). For the purpose of designing a similar product with easy installation, a novel radiative HX is introduced. The radiative HX has a similar structure to the chilled ceiling panels, which include serpentine-shaped tubes fixed on metal sheets. The tubes filled with working fluid such as water serve as heating/cooling source and conduct heat to the metal sheets. The metal sheets condition the space air through both natural convection and radiation. An attractive feature of the radiative HXs is that instead of installing them over the ceiling or under the floor, the HX can be simply installed against walls (see Figure 2). Such installation method has a two-fold benefit: easy installation and capability of providing both heating and cooling. This paper discusses the modeling of the radiative HXs so that it can be used as a tool to evaluate the thermal comfort in a zone equipped with such HXs.

3 2324, Page 2 Figure 1: Picture of piping for heated floor system during installation (Olesen, 2011) Figure 2: Picture of the radiative HX installed in an office setting 2. RADIATIVE HX THERMAL COMFORT MODELING The objective of the simulation tool development is to evaluate the thermal comfort condition of the entire space conditioned by the radiative HX. In the modeling, the radiative HX is assumed to control the temperature of the entire wall being installed. The modeling includes two major efforts: the simulation of operative temperature (OT) field and the evaluation of ASHRAE s thermal comfort criteria. According to the ASHRAE standard 55 (2004), OT is a combination of mean radiant temperature (MRT) and air temperature. In the case of applying the radiative HX, OT calculation can be simplified as the arithmetic mean of MRT and air temperature (Equation 1). In the same standard, two important indices are defined to quantify the thermal comfort criteria: Predicted Mean Vote (PMV) and Predicted Percentage Dissatisfied (PPD). The following subsections provide detailed discussions of the two aforementioned modeling efforts. / for high air velocity /2 for low air velocity (1) 2.1 OT Modeling As mentioned before, OT is the combination of MRT and air temperature. Figure 3 describes the radiation model adopted in the study. The room is assumed to be a rectangular shape with four walls (front wall is not shown), a ceiling and a floor. One wall is assumed to have the radiative HX (left wall in the Figure 3). It is assumed that the HX covers the entire wall and maintained a constant temperature. It should be noted that the later experiment demonstrated a 2K temperature difference between inlet and outlet water flow (Koepke, 2011), therefore the assumption of a constant temperature profile is a simplified one compared to the real case. Other walls may have different temperatures, and so may the ceiling and the floor. Window usually has different temperature compared to

4 2324, Page 3 the wall where it is located, which is mainly due to the solar radiation. Equation 2 (Arora, 2000) is then applied to calculate the window temperature. It should be noted that the solar incidence in the equation varies with solar angles and window orientation. Therefore, local solar angles such as solar azimuth angle, solar altitude angle should be identified beforehand. As all surface temperatures (wall temperatures, ceiling and floor temperatures, window temperature etc.) are obtained, the MRT can be evaluated by the summation of the view factors between the occupant and individual surface multiplied by the surface temperature. For simplification, the occupant in the room is simplified to be a sphere. Dunkle (1963) defined the equivalent sphere radius of both a standing person and a sitting person. However, since the sphere s radius is infinitesimal compared with the room dimension, the sphere was further simplified to be a dot. Since occupants can move inside the space, the evaluation of their thermal comfort requires calculation of MRT everywhere inside the space, which means that an MRT field has to be obtained. 0 0 (2) Figure 3: Adapted model for radiant temperature field The other component of OT calculation is the air temperature simulation. The technique of computational fluid dynamic (CFD) is utilized for air temperature field simulation inside the space. A commercially-available CFD (ANSYS, 2006) package was chosen for the modeling. As an example to facilitate initial research, 2D square was assumed to represent the vertical middle inter-section plane of the space. It has one cold side (left side) of 20 C which can be assumed as a case of the radiative HX filled with cold water to provide cooling, and one hot side (right side) of 35 C which can be assumed as a case of hot window by direct solar radiation. The square has a mesh of 240 by 240 quad cells with enhanced mesh density in the boundary layer to capture the complicated flow characteristics. To be specific, the boundary layer has the first row of 1 mm and the growth of 1.15, i.e., the entire depth of the boundary layer is 20 mm. The turbulence model used in the model is k-ω SST model. The velocity (streamline) and temperature field are demonstrated in Figure 4. Figure 4: The streamline (velocity, left) and air temperature (right) fields in the studied place

5 2324, Page 4 Although the example proves that the CFD simulation can be applied to simulate the air temperature field, the computation cost is high. It would be better to develop a reduced-order modeling method allowing a good compromise between the accuracy and the computation cost. The proper orthogonal decomposition (POD) was chosen as the reduced-order model to replace the above CFD simulation. The POD method was first introduced by John Lumley (Berkooz et al., 1993). In other disciplines the same method was called as Karhunen-Loève decomposition or principal components analysis. It has several advantages as pointed out by Berkooz et al. (1993): (1) It is statistically based-extracting data from experiments and simulations. (2) Its analytical foundations supply a clear understanding of its capabilities and limitations. (3) It permits the extraction of the results. The flow chart of the POD method is shown in Figure 5. In short, the method seeks to decompose a large degree of freedom system into a series of expansion as shown in Equation (3)., (3) Figure 5: Flow chart of POD method After skipping the detailed extreme computing, it turns out that the basis functions (φ) are the Eigen functions of the integral equation (Ly and Hein, 2001):, (4) where the kernel C is given by:, (5) For the current problem, in order to obtain the POD modes for the air temperature field, a technique called snapshot was applied to form the matrix C by utilizing the existing CFD simulation results. Nine sets of temperature fields and velocity fields were chosen to form the snapshot. The difference among each snapshot is the different Rayleigh numbers. The CFD software package is used to calculate the eigenvalues of the kernel matrix C. The built-in singular value decomposition (SVD) function was applied to return the eigenvalues and the corresponding eigenvectors. If the eigenvalue is zero meaning that it poses no impact on the system anymore, therefore its corresponding eigenvector is neglected. The proper orthogonal decomposition provides the basis of the expansion series. The next step is to find the coefficients in the expansion (Equation 3). A method called Galerkin projection is considered to be a standard approach to obtain the coefficients. The method projects the governing equations on the modal subspace and then solves the governing equations, usually in the form of ODE equations to obtain the coefficients.

6 2324, Page PMV and PPD Field Simulation The previous subsection discusses the simulation of both MRT and air temperature. By simply averaging those two, one can obtain the OT field. However, it is not straightforward to use OT to describe the thermal comfort. Therefore, the PMV and PPD fields are then simulated by the software tool. The PMV is a seven-scale system to describe occupant s thermal sensation from very hot (+3) to very cold (-3). The PPD is its derivative to statistically show how much percentage of occupants feel uncomfortable at different PMV scale. Table 1 and Figure 6 describe the PMV and PPD, respectively, in more detail. To calculate the PMV, Equation 6 is used. Although including many parameters, most of which in the equation can be obtained from the ISO standard 7730 (2005). The air temperature and MRT can be calculated by methods summarized in the previous section. The PPD can be calculated based on the Equation 7. Figures 7 and 8 show sample outputs of PMV and PPD from the tool, respectively. As shown, both left and right side are affected by the hot wall and hot window as well as larger vertical air velocity than that in the middle, so the PMV indices near the walls are between slightly warm and warm. Due to the density difference of air, the cold air remains at the bottom and the hot air remains at the top of the space. Consequently the PMV field shows negative numbers at the bottom and positive numbers at the top of the space. Although there are differences in PMV values inside the space, most of which are between -1 and +1 meaning thermal comfort to the occupants. This is supported by the PPD output, which shows that only 5% thermal discomfort rate is predicted for most of the space (6) exp (7) Table 1: PMV scale (ISO 7730, 2005) PMV scale Thermal sensation +3 hot +2 warm +1 slightly warm 0 neutral -1 slightly cool -2 cool -3 cold Figure 6: PPD as a function of PMV (ISO 7730, 2005)

7 2324, Page 6 Figure 7: Snapshots of sample PMV output Figure 8: Snapshots of sample PPD output 3. SOFTWARE VALIDATION The lack of PMV/PPD sensors limits the validation of the tool to the OT temperature only. In order to verify the correctness of the POD simulations, two cases of POD calculation results were compared to those from CFD simulation. Case 1 is solving for air temperature inside a 3 m by 3 m square enclosure with the Rayleigh number of Case 2 is solving for the same problem with the Rayleigh number of Figure 9 demonstrates the comparison results. The 3 m by 3 m enclosure is divided into 225 cells. The x-axis represents the 225 cells. For example, the top left cell is number 1, the rightmost cell of the top row is number 15, and the right bottom cell is number 225. The temperature results in each cell were compared to those from the CFD simulation. Both POD cases show good

8 2324, Page 7 agreement to the CFD simulations. In Case 1, the maximum deviation is only 0.04K, while in Case 2, the maximum deviation is around 0.1K. It demonstrates that the POD calculation provides enough accuracy compared with CFD calculation. Considering the fact that it takes only several minutes for the POD codes to solve all the ODE functions and to output the results, the benefit of using POD is very clear. However, the fast speed depends on the existence of snapshots. The first preparation of snapshots may take a week, and then the POD calculation can solve any problem within the range of snapshots. Figure 9: Difference in air temperature from POD and CFD simulation (left Ra = 10 6, right Ra=10 9 ) The simulated OT field was then compared to experimental data. Figure 10 shows the comparison results. The OTmeasuring facility was located in the center of the room with four OT sensors installed at different heights. The average deviation between the two results is only 0.4K. It demonstrates that the reduced-order model and the radiation model together provide a good prediction of the OT field inside the cubic office room setting. Figure 10: Comparison of OT from experiment and simulation 4. CONCLUSIONS In order to reduce the fan power consumption, the radiative heat exchanger was proposed to be a new indoor heat exchanger design for low temperature lift heat pump systems. The current study focuses on the development of a radiative HX modeling tool. The operative temperature and velocity field in an office setting equipped with radiative heat exchanger was simulated. The model was able to calculate the operative temperature, air velocity, PMV and PPD indices everywhere in the office. The CFD simulation which was used to calculate the air temperature and air

9 2324, Page 8 velocity was later replaced by a reduced-order method called POD. Using POD, the computation cost was greatly reduced while still maintaining enough accuracy compared to CFD. The simulated operative temperature field of the office setting was compared to experimental data. The average deviation between modeling results and experimental data was 0.4K thus proving the efficacy of the model. Since the POD method takes Rayleigh number as an input, the snapshots can be re-used for analyzing other cases of different temperature differences and dimensions with the similar Rayleigh number. NOMENCLATURE a POD coefficient (-) Subscripts A Area m 2 a air f cl Clothing factor (-) c convective h Heat transfer coefficient W/K cl clothing I Solar incidence W d diffusive M metabolic rate W D direct Pa Water vapor partial pressure Pa g glass t air temperature C i inside v Velocity or temperature m/s or C o operative/outside W work output W r radiative α Absorptivity (-) φ POD basis (-) REFERENCES ANSYS, Inc., Fluent version ANSYS, Inc., Gambit version Arora. C.P., 2000, Refrigeration and Air Conditioning, Second Edition, Chapter 17, pp ASHRAE., ANSI/ARI Standard : Thermal Environmental Conditions for Human Occupancy. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers Inc. Berkooz, G., Holmes, P., and Lumley, J., The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech., 33, Dunkle, R., Configuration factors for radiant heat transfer calculations involving people. Journal of Heat Transfer, ISO., ISO standard 7730: 2005, Ergonomics of the thermal environment Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria. Geneva: International Organization for Standardization. Koepke, M., Experimental investigations on the thermal comfort of an office setting conditioned by low ΔT heat exchangers, Bachelor thesis, University of Maryland, College Park and Technische Universität Berlin Ling, J., Hwang, Y., Radermacher, R., Theoretical study on separate sensible and latent cooling airconditioning system. International Journal of Refrigeration, 33(3), Ly, H. V., and Hein, T. T., Modeling and control of physical processes using proper orthogonal decomposition. Math. Comput. Modelling, 33, Olesen, B., Low Temperature Radiant Heating High Temperature Radiant Cooling, Technical University of Denmark, ASHRAE Learning Institute, ACKNOWLEDGEMENTS We gratefully acknowledge the support of this effort from the sponsors of the Alternative Cooling Technologies and Applications Consortium and the Center for Environmental Energy Engineering (CEEE) at the University of Maryland.